Interesting Links (example problem):

A car-truck collision

These can be very complex. On page 207, Serway discusses an two-dimensional elastic glancing collision.  This is a good example to study.

The same principles apply as for one-dimensional collisions:

conservation of momentum (two scalar equations can be written; for x & for y)
conservation of kinetic energy (energy is a scalar, so there's only one equation)

Set up a coordinate system, choosing it in line with the initial motion so that there are no y and z-components for the initial motion (if possible)

Use subscripts to represent the unknown velocities
Write the equations

Count the unknowns. If there are more than you have equations, don't bother going further.

The bodies stick together after collision or, in the case of an explosion, they are one body initially and two or more afterward. In the first case, the final velocity of one is the same as the other; use one symbol (not two) to represent these velocities.

Impulse and Momentum:

The principle is the same as for one-dimensional collisions: average force times the time equals the impulse, which equals the change in the momentum (of one body). It's often easier to use the full vector symbolism rather than split the directions and use two scalar equations.

Example 1: Tiger Woods you're not!

Example 2: An explosion

Example 3: Serway's Example 9.13